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cgal/Triangulation_3/include/CGAL/Triangulation_3.h

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// Copyright (c) 1999-2003 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s) : Monique Teillaud <Monique.Teillaud@sophia.inria.fr>
// Sylvain Pion
#ifndef CGAL_TRIANGULATION_3_H
#define CGAL_TRIANGULATION_3_H
#include <CGAL/basic.h>
#include <iostream>
#include <list>
#include <set>
#include <map>
#include <utility>
#include <stack>
#include <CGAL/triangulation_assertions.h>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/Triangulation_data_structure_3.h>
#include <CGAL/Triangulation_cell_base_3.h>
#include <CGAL/Triangulation_vertex_base_3.h>
#include <CGAL/spatial_sort.h>
#include <CGAL/iterator.h>
#include <CGAL/function_objects.h>
#include <CGAL/Iterator_project.h>
#include <CGAL/Random.h>
#include <CGAL/Unique_hash_map.h>
#include <boost/bind.hpp>
CGAL_BEGIN_NAMESPACE
template < class GT, class Tds > class Triangulation_3;
template < class GT, class Tds > std::istream& operator>>
(std::istream& is, Triangulation_3<GT,Tds> &tr);
template < class GT,
class Tds = Triangulation_data_structure_3 <
Triangulation_vertex_base_3<GT>,
Triangulation_cell_base_3<GT> > >
class Triangulation_3
:public Triangulation_utils_3
{
friend std::istream& operator>> <>
(std::istream& is, Triangulation_3<GT,Tds> &tr);
typedef Triangulation_3<GT, Tds> Self;
public:
typedef Tds Triangulation_data_structure;
typedef GT Geom_traits;
typedef typename GT::Point_3 Point;
typedef typename GT::Segment_3 Segment;
typedef typename GT::Triangle_3 Triangle;
typedef typename GT::Tetrahedron_3 Tetrahedron;
typedef typename Tds::Vertex Vertex;
typedef typename Tds::Cell Cell;
typedef typename Tds::Facet Facet;
typedef typename Tds::Edge Edge;
typedef typename Tds::size_type size_type;
typedef typename Tds::difference_type difference_type;
typedef typename Tds::Vertex_handle Vertex_handle;
typedef typename Tds::Cell_handle Cell_handle;
typedef typename Tds::Cell_circulator Cell_circulator;
typedef typename Tds::Facet_circulator Facet_circulator;
typedef typename Tds::Cell_iterator Cell_iterator;
typedef typename Tds::Facet_iterator Facet_iterator;
typedef typename Tds::Edge_iterator Edge_iterator;
typedef typename Tds::Vertex_iterator Vertex_iterator;
typedef Cell_iterator All_cells_iterator;
typedef Facet_iterator All_facets_iterator;
typedef Edge_iterator All_edges_iterator;
typedef Vertex_iterator All_vertices_iterator;
typedef typename Tds::Simplex Simplex;
private:
// This class is used to generate the Finite_*_iterators.
class Infinite_tester
{
const Self *t;
public:
Infinite_tester() {}
Infinite_tester(const Self *tr)
: t(tr) {}
bool operator()(const Vertex_iterator & v) const
{
return t->is_infinite(v);
}
bool operator()(const Cell_iterator & c) const
{
return t->is_infinite(c);
}
bool operator()(const Edge_iterator & e) const
{
return t->is_infinite(*e);
}
bool operator()(const Facet_iterator & f) const
{
return t->is_infinite(*f);
}
};
public:
// We derive in order to add a conversion to handle.
class Finite_cells_iterator
: public Filter_iterator<Cell_iterator, Infinite_tester> {
typedef Filter_iterator<Cell_iterator, Infinite_tester> Base;
typedef Finite_cells_iterator Self;
public:
Finite_cells_iterator() : Base() {}
Finite_cells_iterator(const Base &b) : Base(b) {}
Self & operator++() { Base::operator++(); return *this; }
Self & operator--() { Base::operator--(); return *this; }
Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
operator Cell_handle() const { return Base::base(); }
};
// We derive in order to add a conversion to handle.
class Finite_vertices_iterator
: public Filter_iterator<Vertex_iterator, Infinite_tester> {
typedef Filter_iterator<Vertex_iterator, Infinite_tester> Base;
typedef Finite_vertices_iterator Self;
public:
Finite_vertices_iterator() : Base() {}
Finite_vertices_iterator(const Base &b) : Base(b) {}
Self & operator++() { Base::operator++(); return *this; }
Self & operator--() { Base::operator--(); return *this; }
Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
operator Vertex_handle() const { return Base::base(); }
};
typedef Filter_iterator<Edge_iterator, Infinite_tester>
Finite_edges_iterator;
typedef Filter_iterator<Facet_iterator, Infinite_tester>
Finite_facets_iterator;
private:
// Auxiliary iterators for convenience
// do not use default template argument to please VC++
typedef Project_point<Vertex> Proj_point;
public:
typedef Iterator_project<Finite_vertices_iterator,
Proj_point,
const Point&,
const Point*,
std::ptrdiff_t,
std::bidirectional_iterator_tag> Point_iterator;
typedef Point value_type; // to have a back_inserter
typedef const value_type& const_reference;
//Tag to distinguish triangulations with weighted_points
typedef Tag_false Weighted_tag;
enum Locate_type {
VERTEX=0,
EDGE, //1
FACET, //2
CELL, //3
OUTSIDE_CONVEX_HULL, //4
OUTSIDE_AFFINE_HULL };//5
protected:
Tds _tds;
GT _gt;
Vertex_handle infinite; //infinite vertex
mutable Random rng;
Comparison_result
compare_xyz(const Point &p, const Point &q) const
{
return geom_traits().compare_xyz_3_object()(p, q);
}
bool
equal(const Point &p, const Point &q) const
{
return compare_xyz(p, q) == EQUAL;
}
Orientation
orientation(const Point &p, const Point &q,
const Point &r, const Point &s) const
{
return geom_traits().orientation_3_object()(p, q, r, s);
}
bool
coplanar(const Point &p, const Point &q,
const Point &r, const Point &s) const
{
return orientation(p, q, r, s) == COPLANAR;
}
Orientation
coplanar_orientation(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().coplanar_orientation_3_object()(p, q, r);
}
bool
collinear(const Point &p, const Point &q, const Point &r) const
{
return coplanar_orientation(p, q, r) == COLLINEAR;
}
Segment
construct_segment(const Point &p, const Point &q) const
{
return geom_traits().construct_segment_3_object()(p, q);
}
Triangle
construct_triangle(const Point &p, const Point &q, const Point &r) const
{
return geom_traits().construct_triangle_3_object()(p, q, r);
}
Tetrahedron
construct_tetrahedron(const Point &p, const Point &q,
const Point &r, const Point &s) const
{
return geom_traits().construct_tetrahedron_3_object()(p, q, r, s);
}
enum COLLINEAR_POSITION {BEFORE, SOURCE, MIDDLE, TARGET, AFTER};
COLLINEAR_POSITION
collinear_position(const Point &s, const Point &p, const Point &t) const
// (s,t) defines a line, p is on that line.
// Depending on the position of p wrt s and t, returns :
// --------------- s ---------------- t --------------
// BEFORE SOURCE MIDDLE TARGET AFTER
{
CGAL_triangulation_precondition(!equal(s, t));
CGAL_triangulation_precondition(collinear(s, p, t));
Comparison_result ps = compare_xyz(p, s);
if (ps == EQUAL)
return SOURCE;
Comparison_result st = compare_xyz(s, t);
if (ps == st)
return BEFORE;
Comparison_result pt = compare_xyz(p, t);
if (pt == EQUAL)
return TARGET;
if (pt == st)
return MIDDLE;
return AFTER;
}
void init_tds()
{
infinite = _tds.insert_increase_dimension();
}
public:
// CONSTRUCTORS
Triangulation_3(const GT & gt = GT())
: _tds(), _gt(gt)
{
init_tds();
}
// copy constructor duplicates vertices and cells
Triangulation_3(const Triangulation_3 & tr)
: _gt(tr._gt)
{
infinite = _tds.copy_tds(tr._tds, tr.infinite);
CGAL_triangulation_expensive_postcondition(*this == tr);
}
template < typename InputIterator >
Triangulation_3(InputIterator first, InputIterator last,
const GT & gt = GT())
: _gt(gt)
{
init_tds();
insert(first, last);
}
void clear()
{
_tds.clear();
init_tds();
}
Triangulation_3 & operator=(Triangulation_3 tr)
{
swap(tr);
return *this;
}
// HELPING FUNCTIONS
void swap(Triangulation_3 &tr)
{
std::swap(tr._gt, _gt);
std::swap(tr.infinite, infinite);
_tds.swap(tr._tds);
}
//ACCESS FUNCTIONS
const GT & geom_traits() const
{ return _gt;}
const Tds & tds() const
{ return _tds;}
Tds & tds()
{ return _tds;}
int dimension() const
{ return _tds.dimension();}
size_type number_of_finite_cells() const;
size_type number_of_cells() const;
size_type number_of_finite_facets() const;
size_type number_of_facets() const;
size_type number_of_finite_edges() const;
size_type number_of_edges() const;
size_type number_of_vertices() const // number of finite vertices
{return _tds.number_of_vertices()-1;}
Vertex_handle infinite_vertex() const
{ return infinite; }
Cell_handle infinite_cell() const
{
CGAL_triangulation_assertion(infinite_vertex()->cell()->
has_vertex(infinite_vertex()));
return infinite_vertex()->cell();
}
// GEOMETRIC ACCESS FUNCTIONS
Tetrahedron tetrahedron(const Cell_handle c) const
{
CGAL_triangulation_precondition( dimension() == 3 );
CGAL_triangulation_precondition( ! is_infinite(c) );
return construct_tetrahedron(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point());
}
Triangle triangle(const Cell_handle c, int i) const;
Triangle triangle(const Facet & f) const
{ return triangle(f.first, f.second); }
Segment segment(const Cell_handle c, int i, int j) const;
Segment segment(const Edge & e) const
{ return segment(e.first,e.second,e.third); }
// TEST IF INFINITE FEATURES
bool is_infinite(const Vertex_handle v) const
{ return v == infinite_vertex(); }
bool is_infinite(const Cell_handle c) const
{
CGAL_triangulation_precondition( dimension() == 3 );
return c->has_vertex(infinite_vertex());
}
bool is_infinite(const Cell_handle c, int i) const;
bool is_infinite(const Facet & f) const
{ return is_infinite(f.first,f.second); }
bool is_infinite(const Cell_handle c, int i, int j) const;
bool is_infinite(const Edge & e) const
{ return is_infinite(e.first,e.second,e.third); }
//QUERIES
bool is_vertex(const Point & p, Vertex_handle & v) const;
bool is_vertex(Vertex_handle v) const;
bool is_edge(Vertex_handle u, Vertex_handle v,
Cell_handle & c, int & i, int & j) const;
bool is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle & c, int & i, int & j, int & k) const;
bool is_cell(Cell_handle c) const;
bool is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c, int & i, int & j, int & k, int & l) const;
bool is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c) const;
bool has_vertex(const Facet & f, Vertex_handle v, int & j) const;
bool has_vertex(Cell_handle c, int i, Vertex_handle v, int & j) const;
bool has_vertex(const Facet & f, Vertex_handle v) const;
bool has_vertex(Cell_handle c, int i, Vertex_handle v) const;
bool are_equal(Cell_handle c, int i, Cell_handle n, int j) const;
bool are_equal(const Facet & f, const Facet & g) const;
bool are_equal(const Facet & f, Cell_handle n, int j) const;
Cell_handle
locate(const Point & p,
Locate_type & lt, int & li, int & lj,
Cell_handle start = Cell_handle()) const;
Cell_handle
locate(const Point & p, Cell_handle start = Cell_handle()) const
{
Locate_type lt;
int li, lj;
return locate( p, lt, li, lj, start);
}
Cell_handle
locate(const Point & p,
Locate_type & lt, int & li, int & lj, Vertex_handle hint) const
{
return locate(p, lt, li, lj, hint == Vertex_handle() ? infinite_cell() : hint->cell());
}
Cell_handle
locate(const Point & p, Vertex_handle hint) const
{
return locate(p, hint == Vertex_handle() ? infinite_cell() : hint->cell());
}
// PREDICATES ON POINTS ``TEMPLATED'' by the geom traits
Bounded_side
side_of_tetrahedron(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
const Point & p3,
Locate_type & lt, int & i, int & j ) const;
Bounded_side
side_of_cell(const Point & p,
Cell_handle c,
Locate_type & lt, int & i, int & j) const;
Bounded_side
side_of_triangle(const Point & p,
const Point & p0, const Point & p1, const Point & p2,
Locate_type & lt, int & i, int & j ) const;
Bounded_side
side_of_facet(const Point & p,
Cell_handle c,
Locate_type & lt, int & li, int & lj) const;
Bounded_side
side_of_facet(const Point & p,
const Facet & f,
Locate_type & lt, int & li, int & lj) const
{
CGAL_triangulation_precondition( f.second == 3 );
return side_of_facet(p, f.first, lt, li, lj);
}
Bounded_side
side_of_segment(const Point & p,
const Point & p0, const Point & p1,
Locate_type & lt, int & i ) const;
Bounded_side
side_of_edge(const Point & p,
Cell_handle c,
Locate_type & lt, int & li) const;
Bounded_side
side_of_edge(const Point & p,
const Edge & e,
Locate_type & lt, int & li) const
{
CGAL_triangulation_precondition( e.second == 0 );
CGAL_triangulation_precondition( e.third == 1 );
return side_of_edge(p, e.first, lt, li);
}
// Functions forwarded from TDS.
int mirror_index(Cell_handle c, int i) const
{ return _tds.mirror_index(c, i); }
Vertex_handle mirror_vertex(Cell_handle c, int i) const
{ return _tds.mirror_vertex(c, i); }
Facet mirror_facet(Facet f) const
{ return _tds.mirror_facet(f);}
// MODIFIERS
bool flip(const Facet &f)
// returns false if the facet is not flippable
// true other wise and
// flips facet i of cell c
// c will be replaced by one of the new cells
{
return flip( f.first, f.second);
}
bool flip(Cell_handle c, int i);
void flip_flippable(const Facet &f)
{
flip_flippable( f.first, f.second);
}
void flip_flippable(Cell_handle c, int i);
bool flip(const Edge &e)
// returns false if the edge is not flippable
// true otherwise and
// flips edge i,j of cell c
// c will be deleted
{
return flip( e.first, e.second, e.third );
}
bool flip(Cell_handle c, int i, int j);
void flip_flippable(const Edge &e)
{
flip_flippable( e.first, e.second, e.third );
}
void flip_flippable(Cell_handle c, int i, int j);
//INSERTION
Vertex_handle insert(const Point & p, Vertex_handle hint)
{
return insert(p, hint == Vertex_handle() ? infinite_cell() : hint->cell());
}
Vertex_handle insert(const Point & p, Cell_handle start = Cell_handle());
Vertex_handle insert(const Point & p, Locate_type lt, Cell_handle c,
int li, int lj);
template < class Conflict_tester, class Hidden_points_visitor >
inline Vertex_handle insert_in_conflict(const Point & p,
Locate_type lt,
Cell_handle c, int li, int lj,
const Conflict_tester &tester,
Hidden_points_visitor &hider);
template < class InputIterator >
int insert(InputIterator first, InputIterator last)
{
int n = number_of_vertices();
std::vector<Point> points (first, last);
std::random_shuffle (points.begin(), points.end());
spatial_sort (points.begin(), points.end(), geom_traits());
Vertex_handle hint;
for (typename std::vector<Point>::const_iterator p = points.begin(), end = points.end();
p != end; ++p)
hint = insert(*p, hint);
return number_of_vertices() - n;
}
Vertex_handle
insert_in_cell(const Point & p, Cell_handle c);
Vertex_handle
insert_in_facet(const Point & p, Cell_handle c, int i);
Vertex_handle
insert_in_facet(const Point & p, const Facet & f)
{
return insert_in_facet(p, f.first, f.second);
}
Vertex_handle
insert_in_edge(const Point & p, Cell_handle c, int i, int j);
Vertex_handle
insert_in_edge(const Point & p, const Edge & e)
{
return insert_in_edge(p, e.first, e.second, e.third);
}
Vertex_handle
insert_outside_convex_hull(const Point & p, Cell_handle c);
Vertex_handle
insert_outside_affine_hull(const Point & p);
template <class CellIt>
Vertex_handle
insert_in_hole(const Point & p, CellIt cell_begin, CellIt cell_end,
Cell_handle begin, int i)
{
// Some geometric preconditions should be tested...
Vertex_handle v = _tds.insert_in_hole(cell_begin, cell_end, begin, i);
v->set_point(p);
return v;
}
protected:
// - c is the current cell, which must be in conflict.
// - tester is the function object that tests if a cell is in conflict.
//
// in_conflict_flag value :
// 0 -> unknown
// 1 -> in conflict
// 2 -> not in conflict (== on boundary)
template <
class Conflict_test,
class OutputIteratorBoundaryFacets,
class OutputIteratorCells,
class OutputIteratorInternalFacets>
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets>
find_conflicts(Cell_handle d, const Conflict_test &tester,
Triple<OutputIteratorBoundaryFacets,
OutputIteratorCells,
OutputIteratorInternalFacets> it) const
{
CGAL_triangulation_precondition( dimension()>=2 );
CGAL_triangulation_precondition( tester(d) );
std::stack<Cell_handle> cell_stack;
cell_stack.push(d);
d->set_in_conflict_flag(1);
*it.second++ = d;
do {
Cell_handle c = cell_stack.top();
cell_stack.pop();
for (int i=0; i<dimension()+1; ++i) {
Cell_handle test = c->neighbor(i);
if (test->get_in_conflict_flag() == 1) {
if (c < test)
*it.third++ = Facet(c, i); // Internal facet.
continue; // test was already in conflict.
}
if (test->get_in_conflict_flag() == 0) {
if (tester(test)) {
if (c < test)
*it.third++ = Facet(c, i); // Internal facet.
cell_stack.push(test);
test->set_in_conflict_flag(1);
*it.second++ = test;
continue;
}
test->set_in_conflict_flag(2); // test is on the boundary.
}
*it.first++ = Facet(c, i);
}
} while(!cell_stack.empty());
return it;
}
// This one takes a function object to recursively determine the cells in
// conflict, then calls _tds._insert_in_hole().
template < class Conflict_test >
Vertex_handle
insert_conflict(Cell_handle c, const Conflict_test &tester)
{
CGAL_triangulation_precondition( dimension() >= 2 );
CGAL_triangulation_precondition( c != Cell_handle() );
CGAL_triangulation_precondition( tester(c) );
std::vector<Cell_handle> cells;
cells.reserve(32);
Facet facet;
// Find the cells in conflict
switch (dimension()) {
case 3:
find_conflicts(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
break;
case 2:
find_conflicts(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
}
// Create the new cells and delete the old.
return _tds._insert_in_hole(cells.begin(), cells.end(),
facet.first, facet.second);
}
private:
// Here are the conflit tester function objects passed to
// insert_conflict_[23]() by insert_outside_convex_hull().
class Conflict_tester_outside_convex_hull_3
{
const Point &p;
const Self *t;
public:
Conflict_tester_outside_convex_hull_3(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
Locate_type loc;
int i, j;
return t->side_of_cell( p, c, loc, i, j ) == ON_BOUNDED_SIDE;
}
};
class Conflict_tester_outside_convex_hull_2
{
const Point &p;
const Self *t;
public:
Conflict_tester_outside_convex_hull_2(const Point &pt, const Self *tr)
: p(pt), t(tr) {}
bool operator()(const Cell_handle c) const
{
Locate_type loc;
int i, j;
return t->side_of_facet( p, c, loc, i, j ) == ON_BOUNDED_SIDE;
}
};
protected:
// test_dim_down needs to be protected because it is used by the
// ear algorithm in Delaunay_triangulation_3
bool test_dim_down(Vertex_handle v) const;
template < class VertexRemover >
void remove(Vertex_handle v, VertexRemover &remover);
private:
typedef Facet Edge_2D;
typedef Triple<Vertex_handle,Vertex_handle,Vertex_handle> Vertex_triple;
Vertex_triple make_vertex_triple(const Facet& f) const;
void make_canonical(Vertex_triple& t) const;
template < class VertexRemover >
VertexRemover& make_hole_2D(Vertex_handle v, std::list<Edge_2D> & hole,
VertexRemover &remover);
template < class VertexRemover >
void fill_hole_2D(std::list<Edge_2D> & hole, VertexRemover &remover);
void make_hole_3D( Vertex_handle v, std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle> & hole);
template < class VertexRemover >
VertexRemover& remove_dim_down(Vertex_handle v, VertexRemover &remover);
template < class VertexRemover >
VertexRemover& remove_1D(Vertex_handle v, VertexRemover &remover);
template < class VertexRemover >
VertexRemover& remove_2D(Vertex_handle v, VertexRemover &remover);
template < class VertexRemover >
VertexRemover& remove_3D(Vertex_handle v, VertexRemover &remover);
// They access "Self", so need to be friend.
friend class Conflict_tester_outside_convex_hull_3;
friend class Conflict_tester_outside_convex_hull_2;
friend class Infinite_tester;
friend class Finite_vertices_iterator;
friend class Finite_cells_iterator;
public:
//TRAVERSING : ITERATORS AND CIRCULATORS
Finite_cells_iterator finite_cells_begin() const
{
if ( dimension() < 3 )
return finite_cells_end();
return CGAL::filter_iterator(cells_end(), Infinite_tester(this),
cells_begin());
}
Finite_cells_iterator finite_cells_end() const
{
return CGAL::filter_iterator(cells_end(), Infinite_tester(this));
}
Cell_iterator cells_begin() const
{
return _tds.cells_begin();
}
Cell_iterator cells_end() const
{
return _tds.cells_end();
}
All_cells_iterator all_cells_begin() const
{
return _tds.cells_begin();
}
All_cells_iterator all_cells_end() const
{
return _tds.cells_end();
}
Finite_vertices_iterator finite_vertices_begin() const
{
if ( number_of_vertices() <= 0 )
return finite_vertices_end();
return CGAL::filter_iterator(vertices_end(), Infinite_tester(this),
vertices_begin());
}
Finite_vertices_iterator finite_vertices_end() const
{
return CGAL::filter_iterator(vertices_end(), Infinite_tester(this));
}
Vertex_iterator vertices_begin() const
{
return _tds.vertices_begin();
}
Vertex_iterator vertices_end() const
{
return _tds.vertices_end();
}
All_vertices_iterator all_vertices_begin() const
{
return _tds.vertices_begin();
}
All_vertices_iterator all_vertices_end() const
{
return _tds.vertices_end();
}
Finite_edges_iterator finite_edges_begin() const
{
if ( dimension() < 1 )
return finite_edges_end();
return CGAL::filter_iterator(edges_end(), Infinite_tester(this),
edges_begin());
}
Finite_edges_iterator finite_edges_end() const
{
return CGAL::filter_iterator(edges_end(), Infinite_tester(this));
}
Edge_iterator edges_begin() const
{
return _tds.edges_begin();
}
Edge_iterator edges_end() const
{
return _tds.edges_end();
}
All_edges_iterator all_edges_begin() const
{
return _tds.edges_begin();
}
All_edges_iterator all_edges_end() const
{
return _tds.edges_end();
}
Finite_facets_iterator finite_facets_begin() const
{
if ( dimension() < 2 )
return finite_facets_end();
return CGAL::filter_iterator(facets_end(), Infinite_tester(this),
facets_begin());
}
Finite_facets_iterator finite_facets_end() const
{
return CGAL::filter_iterator(facets_end(), Infinite_tester(this));
}
Facet_iterator facets_begin() const
{
return _tds.facets_begin();
}
Facet_iterator facets_end() const
{
return _tds.facets_end();
}
All_facets_iterator all_facets_begin() const
{
return _tds.facets_begin();
}
All_facets_iterator all_facets_end() const
{
return _tds.facets_end();
}
Point_iterator points_begin() const
{
return Point_iterator(finite_vertices_begin());
}
Point_iterator points_end() const
{
return Point_iterator(finite_vertices_end());
}
// cells around an edge
Cell_circulator incident_cells(const Edge & e) const
{
return _tds.incident_cells(e);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j) const
{
return _tds.incident_cells(c, i, j);
}
Cell_circulator incident_cells(const Edge & e, Cell_handle start) const
{
return _tds.incident_cells(e, start);
}
Cell_circulator incident_cells(Cell_handle c, int i, int j,
Cell_handle start) const
{
return _tds.incident_cells(c, i, j, start);
}
// facets around an edge
Facet_circulator incident_facets(const Edge & e) const
{
return _tds.incident_facets(e);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j) const
{
return _tds.incident_facets(c, i, j);
}
Facet_circulator incident_facets(const Edge & e, const Facet & start) const
{
return _tds.incident_facets(e, start);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j,
const Facet & start) const
{
return _tds.incident_facets(c, i, j, start);
}
Facet_circulator incident_facets(const Edge & e,
Cell_handle start, int f) const
{
return _tds.incident_facets(e, start, f);
}
Facet_circulator incident_facets(Cell_handle c, int i, int j,
Cell_handle start, int f) const
{
return _tds.incident_facets(c, i, j, start, f);
}
// around a vertex
class Finite_filter {
const Self* t;
public:
Finite_filter(const Self* _t): t(_t) {}
template<class T>
bool operator() (const T& e) const {
return t->is_infinite(e);
}
};
class Finite_filter_2D {
const Self* t;
public:
Finite_filter_2D(const Self* _t): t(_t) {}
template<class T>
bool operator() (const T& e) const {
return t->is_infinite(e);
}
bool operator() (const Cell_handle c) {
return t->is_infinite(c, 3);
}
};
template <class OutputIterator>
OutputIterator
incident_cells(Vertex_handle v, OutputIterator cells) const
{
return _tds.incident_cells(v, cells);
}
template <class OutputIterator>
OutputIterator
finite_incident_cells(Vertex_handle v, OutputIterator cells) const
{
if(dimension() == 2)
return _tds.incident_cells(v, cells, Finite_filter_2D(this));
return _tds.incident_cells(v, cells, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator
incident_facets(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets(v, facets);
}
template <class OutputIterator>
OutputIterator
finite_incident_facets(Vertex_handle v, OutputIterator facets) const
{
return _tds.incident_facets(v, facets, Finite_filter(this));
}
// old name (up to CGAL 3.4)
// kept for backwards compatibility but not documented
template <class OutputIterator>
OutputIterator
incident_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices);
}
// correct name
template <class OutputIterator>
OutputIterator
adjacent_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices);
}
// old name (up to CGAL 3.4)
// kept for backwards compatibility but not documented
template <class OutputIterator>
OutputIterator
finite_incident_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices, Finite_filter(this));
}
// correct name
template <class OutputIterator>
OutputIterator
finite_adjacent_vertices(Vertex_handle v, OutputIterator vertices) const
{
return _tds.adjacent_vertices(v, vertices, Finite_filter(this));
}
template <class OutputIterator>
OutputIterator
incident_edges(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges(v, edges);
}
template <class OutputIterator>
OutputIterator
finite_incident_edges(Vertex_handle v, OutputIterator edges) const
{
return _tds.incident_edges(v, edges, Finite_filter(this));
}
size_type degree(Vertex_handle v) const
{
return _tds.degree(v);
}
// CHECKING
bool is_valid(bool verbose = false, int level = 0) const;
bool is_valid(Cell_handle c, bool verbose = false, int level = 0) const;
bool is_valid_finite(Cell_handle c, bool verbose = false, int level=0) const;
};
template < class GT, class Tds >
std::istream &
operator>> (std::istream& is, Triangulation_3<GT, Tds> &tr)
// reads
// the dimension
// the number of finite vertices
// the non combinatorial information on vertices (point, etc)
// the number of cells
// the cells by the indices of their vertices in the preceding list
// of vertices, plus the non combinatorial information on each cell
// the neighbors of each cell by their index in the preceding list of cells
// when dimension < 3 : the same with faces of maximal dimension
{
typedef Triangulation_3<GT, Tds> Triangulation;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Cell_handle Cell_handle;
tr._tds.clear(); // infinite vertex deleted
tr.infinite = tr._tds.create_vertex();
int n, d;
if(is_ascii(is))
is >> d >> n;
else {
read(is, d);
read(is, n);
}
tr._tds.set_dimension(d);
std::map< int, Vertex_handle > V;
V[0] = tr.infinite_vertex();
// the infinite vertex is numbered 0
for (int i=1; i <= n; i++) {
V[i] = tr._tds.create_vertex();
is >> *V[i];
}
std::map< int, Cell_handle > C;
int m;
tr._tds.read_cells(is, V, m, C);
for (int j=0 ; j < m; j++)
is >> *(C[j]);
CGAL_triangulation_assertion( tr.is_valid(false) );
return is;
}
template < class GT, class Tds >
std::ostream &
operator<< (std::ostream& os, const Triangulation_3<GT, Tds> &tr)
// writes :
// the dimension
// the number of finite vertices
// the non combinatorial information on vertices (point, etc)
// the number of cells
// the cells by the indices of their vertices in the preceding list
// of vertices, plus the non combinatorial information on each cell
// the neighbors of each cell by their index in the preceding list of cells
// when dimension < 3 : the same with faces of maximal dimension
{
typedef Triangulation_3<GT, Tds> Triangulation;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Vertex_iterator Vertex_iterator;
typedef typename Triangulation::Cell_iterator Cell_iterator;
typedef typename Triangulation::Edge_iterator Edge_iterator;
typedef typename Triangulation::Facet_iterator Facet_iterator;
// outputs dimension and number of vertices
int n = tr.number_of_vertices();
if (is_ascii(os))
os << tr.dimension() << std::endl << n << std::endl;
else
{
write(os, tr.dimension());
write(os, n);
}
if (n == 0)
return os;
std::vector<Vertex_handle> TV(n+1);
int i = 0;
// write the vertices
for (Vertex_iterator it=tr.vertices_begin(); it!=tr.vertices_end(); ++it)
TV[i++] = it;
CGAL_triangulation_assertion( i == n+1 );
CGAL_triangulation_assertion( tr.is_infinite(TV[0]) );
std::map<Vertex_handle, int > V;
V[tr.infinite_vertex()] = 0;
for (i=1; i <= n; i++) {
os << *TV[i];
V[TV[i]] = i;
if (is_ascii(os))
os << std::endl;
}
// asks the tds for the combinatorial information
tr.tds().print_cells(os, V);
// write the non combinatorial information on the cells
// using the << operator of Cell
// works because the iterator of the tds traverses the cells in the
// same order as the iterator of the triangulation
switch ( tr.dimension() ) {
case 3:
{
for(Cell_iterator it=tr.cells_begin(); it != tr.cells_end(); ++it) {
os << *it; // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
case 2:
{
for(Facet_iterator it=tr.facets_begin(); it != tr.facets_end(); ++it) {
os << *((*it).first); // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
case 1:
{
for(Edge_iterator it=tr.edges_begin(); it != tr.edges_end(); ++it) {
os << *((*it).first); // other information
if(is_ascii(os))
os << std::endl;
}
break;
}
}
return os ;
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_finite_cells() const
{
if ( dimension() < 3 ) return 0;
return std::distance(finite_cells_begin(), finite_cells_end());
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_cells() const
{
return _tds.number_of_cells();
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_finite_facets() const
{
if ( dimension() < 2 ) return 0;
return std::distance(finite_facets_begin(), finite_facets_end());
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_facets() const
{
return _tds.number_of_facets();
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_finite_edges() const
{
if ( dimension() < 1 ) return 0;
return std::distance(finite_edges_begin(), finite_edges_end());
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::size_type
Triangulation_3<GT,Tds>::
number_of_edges() const
{
return _tds.number_of_edges();
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Triangle
Triangulation_3<GT,Tds>::
triangle(const Cell_handle c, int i) const
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3 );
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
CGAL_triangulation_precondition( ! is_infinite(Facet(c, i)) );
if ( (i&1)==0 )
return construct_triangle(c->vertex( (i+2)&3 )->point(),
c->vertex( (i+1)&3 )->point(),
c->vertex( (i+3)&3 )->point());
return construct_triangle(c->vertex( (i+1)&3 )->point(),
c->vertex( (i+2)&3 )->point(),
c->vertex( (i+3)&3 )->point());
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Segment
Triangulation_3<GT,Tds>::
segment(const Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition( i >= 0 && i <= dimension()
&& j >= 0 && j <= dimension() );
CGAL_triangulation_precondition( ! is_infinite(Edge(c, i, j)) );
return construct_segment( c->vertex(i)->point(), c->vertex(j)->point() );
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_infinite(const Cell_handle c, int i) const
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3 );
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
return is_infinite(c->vertex(i<=0 ? 1 : 0)) ||
is_infinite(c->vertex(i<=1 ? 2 : 1)) ||
is_infinite(c->vertex(i<=2 ? 3 : 2));
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_infinite(const Cell_handle c, int i, int j) const
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition(
i >= 0 && i <= dimension() && j >= 0 && j <= dimension() );
return is_infinite( c->vertex(i) ) || is_infinite( c->vertex(j) );
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_vertex(const Point & p, Vertex_handle & v) const
{
Locate_type lt;
int li, lj;
Cell_handle c = locate( p, lt, li, lj );
if ( lt != VERTEX )
return false;
v = c->vertex(li);
return true;
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_vertex(Vertex_handle v) const
{
return _tds.is_vertex(v);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_edge(Vertex_handle u, Vertex_handle v,
Cell_handle & c, int & i, int & j) const
{
return _tds.is_edge(u, v, c, i, j);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_facet(Vertex_handle u, Vertex_handle v, Vertex_handle w,
Cell_handle & c, int & i, int & j, int & k) const
{
return _tds.is_facet(u, v, w, c, i, j, k);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
is_cell(Cell_handle c) const
{
return _tds.is_cell(c);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c, int & i, int & j, int & k, int & l) const
{
return _tds.is_cell(u, v, w, t, c, i, j, k, l);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_cell(Vertex_handle u, Vertex_handle v,
Vertex_handle w, Vertex_handle t,
Cell_handle & c) const
{
int i,j,k,l;
return _tds.is_cell(u, v, w, t, c, i, j, k, l);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(const Facet & f, Vertex_handle v, int & j) const
{
return _tds.has_vertex(f.first, f.second, v, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(Cell_handle c, int i, Vertex_handle v, int & j) const
{
return _tds.has_vertex(c, i, v, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(const Facet & f, Vertex_handle v) const
{
return _tds.has_vertex(f.first, f.second, v);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
has_vertex(Cell_handle c, int i, Vertex_handle v) const
{
return _tds.has_vertex(c, i, v);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(Cell_handle c, int i, Cell_handle n, int j) const
{
return _tds.are_equal(c, i, n, j);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(const Facet & f, const Facet & g) const
{
return _tds.are_equal(f.first, f.second, g.first, g.second);
}
template < class GT, class Tds >
inline
bool
Triangulation_3<GT,Tds>::
are_equal(const Facet & f, Cell_handle n, int j) const
{
return _tds.are_equal(f.first, f.second, n, j);
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Cell_handle
Triangulation_3<GT,Tds>::
locate(const Point & p, Locate_type & lt, int & li, int & lj,
Cell_handle start ) const
// returns the (finite or infinite) cell p lies in
// starts at cell "start"
// if lt == OUTSIDE_CONVEX_HULL, li is the
// index of a facet separating p from the rest of the triangulation
// in dimension 2 :
// returns a facet (Cell_handle,li) if lt == FACET
// returns an edge (Cell_handle,li,lj) if lt == EDGE
// returns a vertex (Cell_handle,li) if lt == VERTEX
// if lt == OUTSIDE_CONVEX_HULL, li, lj give the edge of c
// separating p from the rest of the triangulation
// lt = OUTSIDE_AFFINE_HULL if p is not coplanar with the triangulation
{
if ( dimension() >= 1 ) {
// Make sure we continue from here with a finite cell.
if ( start == Cell_handle() )
start = infinite_cell();
int ind_inf;
if ( start->has_vertex(infinite, ind_inf) )
start = start->neighbor(ind_inf);
}
switch (dimension()) {
case 3:
{
CGAL_triangulation_precondition( start != Cell_handle() );
CGAL_triangulation_precondition( ! start->has_vertex(infinite) );
// We implement the remembering visibility/stochastic walk.
// Remembers the previous cell to avoid useless orientation tests.
Cell_handle previous = Cell_handle();
Cell_handle c = start;
// Stores the results of the 4 orientation tests. It will be used
// at the end to decide if p lies on a face/edge/vertex/interior.
Orientation o[4];
// Now treat the cell c.
try_next_cell:
// We know that the 4 vertices of c are positively oriented.
// So, in order to test if p is seen outside from one of c's facets,
// we just replace the corresponding point by p in the orientation
// test. We do this using the array below.
const Point* pts[4] = { &(c->vertex(0)->point()),
&(c->vertex(1)->point()),
&(c->vertex(2)->point()),
&(c->vertex(3)->point()) };
// For the remembering stochastic walk,
// we need to start trying with a random index :
int i = rng.template get_bits<2>();
// For the remembering visibility walk (Delaunay only), we don't :
// int i = 0;
for (int j=0; j != 4; ++j, i = (i+1)&3) {
Cell_handle next = c->neighbor(i);
if (previous == next) {
o[i] = POSITIVE;
continue;
}
// We temporarily put p at i's place in pts.
const Point* backup = pts[i];
pts[i] = &p;
o[i] = orientation(*pts[0], *pts[1], *pts[2], *pts[3]);
if ( o[i] != NEGATIVE ) {
pts[i] = backup;
continue;
}
if ( next->has_vertex(infinite, li) ) {
// We are outside the convex hull.
lt = OUTSIDE_CONVEX_HULL;
return next;
}
previous = c;
c = next;
goto try_next_cell;
}
// now p is in c or on its boundary
int sum = ( o[0] == COPLANAR )
+ ( o[1] == COPLANAR )
+ ( o[2] == COPLANAR )
+ ( o[3] == COPLANAR );
switch (sum) {
case 0:
{
lt = CELL;
break;
}
case 1:
{
lt = FACET;
li = ( o[0] == COPLANAR ) ? 0 :
( o[1] == COPLANAR ) ? 1 :
( o[2] == COPLANAR ) ? 2 : 3;
break;
}
case 2:
{
lt = EDGE;
li = ( o[0] != COPLANAR ) ? 0 :
( o[1] != COPLANAR ) ? 1 : 2;
lj = ( o[li+1] != COPLANAR ) ? li+1 :
( o[li+2] != COPLANAR ) ? li+2 : li+3;
CGAL_triangulation_assertion(collinear( p,
c->vertex( li )->point(),
c->vertex( lj )->point()));
break;
}
case 3:
{
lt = VERTEX;
li = ( o[0] != COPLANAR ) ? 0 :
( o[1] != COPLANAR ) ? 1 :
( o[2] != COPLANAR ) ? 2 : 3;
break;
}
}
return c;
}
case 2:
{
CGAL_triangulation_precondition( start != Cell_handle() );
CGAL_triangulation_precondition( ! start->has_vertex(infinite) );
Cell_handle c = start;
//first tests whether p is coplanar with the current triangulation
if ( orientation( c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
p ) != DEGENERATE ) {
lt = OUTSIDE_AFFINE_HULL;
li = 3; // only one facet in dimension 2
return c;
}
// if p is coplanar, location in the triangulation
// only the facet numbered 3 exists in each cell
while (1) {
int inf;
if ( c->has_vertex(infinite,inf) ) {
// c must contain p in its interior
lt = OUTSIDE_CONVEX_HULL;
li = cw(inf);
lj = ccw(inf);
return c;
}
// else c is finite
// we test its edges in a random order until we find a
// neighbor to go further
int i = rng.get_int(0, 3);
const Point & p0 = c->vertex( i )->point();
const Point & p1 = c->vertex( ccw(i) )->point();
const Point & p2 = c->vertex( cw(i) )->point();
Orientation o[3];
CGAL_triangulation_assertion(coplanar_orientation(p0,p1,p2)==POSITIVE);
o[0] = coplanar_orientation(p0,p1,p);
if ( o[0] == NEGATIVE ) {
c = c->neighbor( cw(i) );
continue;
}
o[1] = coplanar_orientation(p1,p2,p);
if ( o[1] == NEGATIVE ) {
c = c->neighbor( i );
continue;
}
o[2] = coplanar_orientation(p2,p0,p);
if ( o[2] == NEGATIVE ) {
c = c->neighbor( ccw(i) );
continue;
}
// now p is in c or on its boundary
int sum = ( o[0] == COLLINEAR )
+ ( o[1] == COLLINEAR )
+ ( o[2] == COLLINEAR );
switch (sum) {
case 0:
{
lt = FACET;
li = 3; // useless ?
break;
}
case 1:
{
lt = EDGE;
li = ( o[0] == COLLINEAR ) ? i :
( o[1] == COLLINEAR ) ? ccw(i) :
cw(i);
lj = ccw(li);
break;
}
case 2:
{
lt = VERTEX;
li = ( o[0] != COLLINEAR ) ? cw(i) :
( o[1] != COLLINEAR ) ? i :
ccw(i);
break;
}
}
return c;
}
}
case 1:
{
CGAL_triangulation_precondition( start != Cell_handle() );
CGAL_triangulation_precondition( ! start->has_vertex(infinite) );
Cell_handle c = start;
//first tests whether p is collinear with the current triangulation
if ( ! collinear( p,
c->vertex(0)->point(),
c->vertex(1)->point()) ) {
lt = OUTSIDE_AFFINE_HULL;
return c;
}
// if p is collinear, location :
while (1) {
if ( c->has_vertex(infinite) ) {
// c must contain p in its interior
lt = OUTSIDE_CONVEX_HULL;
return c;
}
// else c is finite
// we test on which direction to continue the traversal
switch (collinear_position(c->vertex(0)->point(),
p,
c->vertex(1)->point()) ) {
case AFTER:
c = c->neighbor(0);
continue;
case BEFORE:
c = c->neighbor(1);
continue;
case MIDDLE:
lt = EDGE;
li = 0;
lj = 1;
return c;
case SOURCE:
lt = VERTEX;
li = 0;
return c;
case TARGET:
lt = VERTEX;
li = 1;
return c;
}
}
}
case 0:
{
Finite_vertices_iterator vit = finite_vertices_begin();
if ( ! equal( p, vit->point() ) ) {
lt = OUTSIDE_AFFINE_HULL;
}
else {
lt = VERTEX;
li = 0;
}
return vit->cell();
}
case -1:
{
lt = OUTSIDE_AFFINE_HULL;
return Cell_handle();
}
default:
{
CGAL_triangulation_assertion(false);
return Cell_handle();
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_tetrahedron(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
const Point & p3,
Locate_type & lt, int & i, int & j ) const
// p0,p1,p2,p3 supposed to be non coplanar
// tetrahedron p0,p1,p2,p3 is supposed to be well oriented
// returns :
// ON_BOUNDED_SIDE if p lies strictly inside the tetrahedron
// ON_BOUNDARY if p lies on one of the facets
// ON_UNBOUNDED_SIDE if p lies strictly outside the tetrahedron
{
CGAL_triangulation_precondition
( orientation(p0,p1,p2,p3) == POSITIVE );
Orientation o0,o1,o2,o3;
if ( ((o0 = orientation(p,p1,p2,p3)) == NEGATIVE) ||
((o1 = orientation(p0,p,p2,p3)) == NEGATIVE) ||
((o2 = orientation(p0,p1,p,p3)) == NEGATIVE) ||
((o3 = orientation(p0,p1,p2,p)) == NEGATIVE) ) {
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
// now all the oi's are >=0
// sum gives the number of facets p lies on
int sum = ( (o0 == ZERO) ? 1 : 0 )
+ ( (o1 == ZERO) ? 1 : 0 )
+ ( (o2 == ZERO) ? 1 : 0 )
+ ( (o3 == ZERO) ? 1 : 0 );
switch (sum) {
case 0:
{
lt = CELL;
return ON_BOUNDED_SIDE;
}
case 1:
{
lt = FACET;
// i = index such that p lies on facet(i)
i = ( o0 == ZERO ) ? 0 :
( o1 == ZERO ) ? 1 :
( o2 == ZERO ) ? 2 :
3;
return ON_BOUNDARY;
}
case 2:
{
lt = EDGE;
// i = smallest index such that p does not lie on facet(i)
// i must be < 3 since p lies on 2 facets
i = ( o0 == POSITIVE ) ? 0 :
( o1 == POSITIVE ) ? 1 :
2;
// j = larger index such that p not on facet(j)
// j must be > 0 since p lies on 2 facets
j = ( o3 == POSITIVE ) ? 3 :
( o2 == POSITIVE ) ? 2 :
1;
return ON_BOUNDARY;
}
case 3:
{
lt = VERTEX;
// i = index such that p does not lie on facet(i)
i = ( o0 == POSITIVE ) ? 0 :
( o1 == POSITIVE ) ? 1 :
( o2 == POSITIVE ) ? 2 :
3;
return ON_BOUNDARY;
}
default:
{
// impossible : cannot be on 4 facets for a real tetrahedron
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_cell(const Point & p,
Cell_handle c,
Locate_type & lt, int & i, int & j) const
// returns
// ON_BOUNDED_SIDE if p inside the cell
// (for an infinite cell this means that p lies strictly in the half space
// limited by its finite facet)
// ON_BOUNDARY if p on the boundary of the cell
// (for an infinite cell this means that p lies on the *finite* facet)
// ON_UNBOUNDED_SIDE if p lies outside the cell
// (for an infinite cell this means that p is not in the preceding
// two cases)
// lt has a meaning only when ON_BOUNDED_SIDE or ON_BOUNDARY
{
CGAL_triangulation_precondition( dimension() == 3 );
if ( ! is_infinite(c) ) {
return side_of_tetrahedron(p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point(),
lt, i, j);
}
else {
int inf = c->index(infinite);
Orientation o;
Vertex_handle
v1=c->vertex((inf+1)&3),
v2=c->vertex((inf+2)&3),
v3=c->vertex((inf+3)&3);
if ( (inf&1) == 0 )
o = orientation(p, v1->point(), v2->point(), v3->point());
else
o = orientation(v3->point(), p, v1->point(), v2->point());
switch (o) {
case POSITIVE:
{
lt = CELL;
return ON_BOUNDED_SIDE;
}
case NEGATIVE:
return ON_UNBOUNDED_SIDE;
case ZERO:
{
// location in the finite facet
int i_f, j_f;
Bounded_side side =
side_of_triangle(p, v1->point(), v2->point(), v3->point(),
lt, i_f, j_f);
// lt need not be modified in most cases :
switch (side) {
case ON_BOUNDED_SIDE:
{
// lt == FACET ok
i = inf;
return ON_BOUNDARY;
}
case ON_BOUNDARY:
{
// lt == VERTEX OR EDGE ok
i = ( i_f == 0 ) ? ((inf+1)&3) :
( i_f == 1 ) ? ((inf+2)&3) :
((inf+3)&3);
if ( lt == EDGE ) {
j = (j_f == 0 ) ? ((inf+1)&3) :
( j_f == 1 ) ? ((inf+2)&3) :
((inf+3)&3);
}
return ON_BOUNDARY;
}
case ON_UNBOUNDED_SIDE:
{
// p lies on the plane defined by the finite facet
// lt must be initialized
return ON_UNBOUNDED_SIDE;
}
default:
{
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
} // switch side
}// case ZERO
default:
{
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
} // switch o
} // else infinite cell
} // side_of_cell
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_triangle(const Point & p,
const Point & p0,
const Point & p1,
const Point & p2,
Locate_type & lt, int & i, int & j ) const
// p0,p1,p2 supposed to define a plane
// p supposed to lie on plane p0,p1,p2
// triangle p0,p1,p2 defines the orientation of the plane
// returns
// ON_BOUNDED_SIDE if p lies strictly inside the triangle
// ON_BOUNDARY if p lies on one of the edges
// ON_UNBOUNDED_SIDE if p lies strictly outside the triangle
{
CGAL_triangulation_precondition( coplanar(p,p0,p1,p2) );
Orientation o012 = coplanar_orientation(p0,p1,p2);
CGAL_triangulation_precondition( o012 != COLLINEAR );
Orientation o0; // edge p0 p1
Orientation o1; // edge p1 p2
Orientation o2; // edge p2 p0
if ((o0 = coplanar_orientation(p0,p1,p)) == opposite(o012) ||
(o1 = coplanar_orientation(p1,p2,p)) == opposite(o012) ||
(o2 = coplanar_orientation(p2,p0,p)) == opposite(o012)) {
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
// now all the oi's are >=0
// sum gives the number of edges p lies on
int sum = ( (o0 == ZERO) ? 1 : 0 )
+ ( (o1 == ZERO) ? 1 : 0 )
+ ( (o2 == ZERO) ? 1 : 0 );
switch (sum) {
case 0:
{
lt = FACET;
return ON_BOUNDED_SIDE;
}
case 1:
{
lt = EDGE;
i = ( o0 == ZERO ) ? 0 :
( o1 == ZERO ) ? 1 :
2;
if ( i == 2 )
j=0;
else
j = i+1;
return ON_BOUNDARY;
}
case 2:
{
lt = VERTEX;
i = ( o0 == o012 ) ? 2 :
( o1 == o012 ) ? 0 :
1;
return ON_BOUNDARY;
}
default:
{
// cannot happen
CGAL_triangulation_assertion(false);
return ON_BOUNDARY;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_facet(const Point & p,
Cell_handle c,
Locate_type & lt, int & li, int & lj) const
// supposes dimension 2 otherwise does not work for infinite facets
// returns :
// ON_BOUNDED_SIDE if p inside the facet
// (for an infinite facet this means that p lies strictly in the half plane
// limited by its finite edge)
// ON_BOUNDARY if p on the boundary of the facet
// (for an infinite facet this means that p lies on the *finite* edge)
// ON_UNBOUNDED_SIDE if p lies outside the facet
// (for an infinite facet this means that p is not in the
// preceding two cases)
// lt has a meaning only when ON_BOUNDED_SIDE or ON_BOUNDARY
// when they mean anything, li and lj refer to indices in the cell c
// giving the facet (c,i)
{
CGAL_triangulation_precondition( dimension() == 2 );
if ( ! is_infinite(c,3) ) {
// The following precondition is useless because it is written
// in side_of_facet
// CGAL_triangulation_precondition( coplanar (p,
// c->vertex(0)->point,
// c->vertex(1)->point,
// c->vertex(2)->point) );
int i_t, j_t;
Bounded_side side = side_of_triangle(p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
lt, i_t, j_t);
// We protect the following code by this test to avoid valgrind messages.
if (side == ON_BOUNDARY) {
// indices in the original cell :
li = ( i_t == 0 ) ? 0 :
( i_t == 1 ) ? 1 : 2;
lj = ( j_t == 0 ) ? 0 :
( j_t == 1 ) ? 1 : 2;
}
return side;
}
// else infinite facet
int inf = c->index(infinite);
// The following precondition is useless because it is written
// in side_of_facet
// CGAL_triangulation_precondition( coplanar (p,
// c->neighbor(inf)->vertex(0)->point(),
// c->neighbor(inf)->vertex(1)->point(),
// c->neighbor(inf)->vertex(2)->point()));
int i2 = next_around_edge(inf,3);
int i1 = 3-inf-i2;
Vertex_handle v1 = c->vertex(i1),
v2 = c->vertex(i2);
CGAL_triangulation_assertion(coplanar_orientation(v1->point(), v2->point(),
mirror_vertex(c, inf)->point()) == POSITIVE);
switch (coplanar_orientation(v1->point(), v2->point(), p)) {
case POSITIVE:
// p lies on the same side of v1v2 as vn, so not in f
return ON_UNBOUNDED_SIDE;
case NEGATIVE:
// p lies in f
lt = FACET;
li = 3;
return ON_BOUNDED_SIDE;
default: // case ZERO:
// p collinear with v1v2
int i_e;
switch (side_of_segment(p, v1->point(), v2->point(), lt, i_e)) {
// computation of the indices in the original cell
case ON_BOUNDED_SIDE:
// lt == EDGE ok
li = i1;
lj = i2;
return ON_BOUNDARY;
case ON_BOUNDARY:
// lt == VERTEX ok
li = ( i_e == 0 ) ? i1 : i2;
return ON_BOUNDARY;
default: // case ON_UNBOUNDED_SIDE:
// p lies on the line defined by the finite edge
return ON_UNBOUNDED_SIDE;
}
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_segment(const Point & p,
const Point & p0,
const Point & p1,
Locate_type & lt, int & i ) const
// p0, p1 supposed to be different
// p supposed to be collinear to p0, p1
// returns :
// ON_BOUNDED_SIDE if p lies strictly inside the edge
// ON_BOUNDARY if p equals p0 or p1
// ON_UNBOUNDED_SIDE if p lies strictly outside the edge
{
CGAL_triangulation_precondition( ! equal(p0, p1) );
CGAL_triangulation_precondition( collinear(p, p0, p1) );
switch (collinear_position(p0, p, p1)) {
case MIDDLE:
lt = EDGE;
return ON_BOUNDED_SIDE;
case SOURCE:
lt = VERTEX;
i = 0;
return ON_BOUNDARY;
case TARGET:
lt = VERTEX;
i = 1;
return ON_BOUNDARY;
default: // case BEFORE: case AFTER:
lt = OUTSIDE_CONVEX_HULL;
return ON_UNBOUNDED_SIDE;
}
}
template < class GT, class Tds >
Bounded_side
Triangulation_3<GT,Tds>::
side_of_edge(const Point & p,
Cell_handle c,
Locate_type & lt, int & li) const
// supposes dimension 1 otherwise does not work for infinite edges
// returns :
// ON_BOUNDED_SIDE if p inside the edge
// (for an infinite edge this means that p lies in the half line
// defined by the vertex)
// ON_BOUNDARY if p equals one of the vertices
// ON_UNBOUNDED_SIDE if p lies outside the edge
// (for an infinite edge this means that p lies on the other half line)
// lt has a meaning when ON_BOUNDED_SIDE and ON_BOUNDARY
// li refer to indices in the cell c
{
CGAL_triangulation_precondition( dimension() == 1 );
if ( ! is_infinite(c,0,1) )
return side_of_segment(p, c->vertex(0)->point(), c->vertex(1)->point(),
lt, li);
// else infinite edge
int inf = c->index(infinite);
switch (collinear_position(c->vertex(1-inf)->point(), p,
mirror_vertex(c, inf)->point())) {
case SOURCE:
lt = VERTEX;
li = 1-inf;
return ON_BOUNDARY;
case BEFORE:
lt = EDGE;
return ON_BOUNDED_SIDE;
default: // case MIDDLE: case AFTER: case TARGET:
return ON_UNBOUNDED_SIDE;
}
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
flip( Cell_handle c, int i )
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() >= 5) );
Cell_handle n = c->neighbor(i);
int in = n->index(c);
if ( is_infinite( c ) || is_infinite( n ) ) return false;
if ( i%2 == 1 ) {
if ( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
}
else {
if ( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
!= POSITIVE ) return false;
}
_tds.flip_flippable(c, i);
return true;
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
flip_flippable( Cell_handle c, int i )
{
CGAL_triangulation_precondition( (dimension() == 3) && (0<=i) && (i<4)
&& (number_of_vertices() >= 5) );
CGAL_triangulation_precondition_code( Cell_handle n = c->neighbor(i); );
CGAL_triangulation_precondition_code( int in = n->index(c); );
CGAL_triangulation_precondition( ( ! is_infinite( c ) ) &&
( ! is_infinite( n ) ) );
if ( i%2 == 1 ) {
CGAL_triangulation_precondition( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
}
else {
CGAL_triangulation_precondition( orientation( c->vertex((i+2)&3)->point(),
c->vertex((i+1)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+3)&3)->point(),
c->vertex((i+2)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
CGAL_triangulation_precondition( orientation( c->vertex((i+1)&3)->point(),
c->vertex((i+3)&3)->point(),
n->vertex(in)->point(),
c->vertex(i)->point() )
== POSITIVE );
}
_tds.flip_flippable(c, i);
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
flip( Cell_handle c, int i, int j )
// flips edge i,j of cell c
{
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() >= 5) );
// checks that degree 3 and not on the convex hull
int degree = 0;
Cell_circulator ccir = incident_cells(c,i,j);
Cell_circulator cdone = ccir;
do {
if ( is_infinite(ccir) ) return false;
++degree;
++ccir;
} while ( ccir != cdone );
if ( degree != 3 ) return false;
// checks that future tetrahedra are well oriented
Cell_handle n = c->neighbor( next_around_edge(i,j) );
int in = n->index( c->vertex(i) );
int jn = n->index( c->vertex(j) );
if ( orientation( c->vertex(next_around_edge(i,j))->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(j)->point() )
!= POSITIVE ) return false;
if ( orientation( c->vertex(i)->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(next_around_edge(i,j))->point() )
!= POSITIVE ) return false;
_tds.flip_flippable(c, i, j);
return true;
}
template < class GT, class Tds >
void
Triangulation_3<GT,Tds>::
flip_flippable( Cell_handle c, int i, int j )
// flips edge i,j of cell c
{
#if !defined CGAL_TRIANGULATION_NO_PRECONDITIONS && \
!defined CGAL_NO_PRECONDITIONS && !defined NDEBUG
CGAL_triangulation_precondition( (dimension() == 3)
&& (0<=i) && (i<4)
&& (0<=j) && (j<4)
&& ( i != j )
&& (number_of_vertices() >= 5) );
int degree = 0;
Cell_circulator ccir = incident_cells(c,i,j);
Cell_circulator cdone = ccir;
do {
CGAL_triangulation_precondition( ! is_infinite(ccir) );
++degree;
++ccir;
} while ( ccir != cdone );
CGAL_triangulation_precondition( degree == 3 );
Cell_handle n = c->neighbor( next_around_edge(i, j) );
int in = n->index( c->vertex(i) );
int jn = n->index( c->vertex(j) );
CGAL_triangulation_precondition
( orientation( c->vertex(next_around_edge(i,j))->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(j)->point() ) == POSITIVE );
CGAL_triangulation_precondition
( orientation( c->vertex(i)->point(),
c->vertex(next_around_edge(j,i))->point(),
n->vertex(next_around_edge(jn,in))->point(),
c->vertex(next_around_edge(i,j))->point() ) == POSITIVE );
#endif
_tds.flip_flippable(c, i, j);
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert(const Point & p, Cell_handle start)
{
Locate_type lt;
int li, lj;
Cell_handle c = locate( p, lt, li, lj, start);
return insert(p, lt, c, li, lj);
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert(const Point & p, Locate_type lt, Cell_handle c, int li, int lj)
{
switch (lt) {
case VERTEX:
return c->vertex(li);
case EDGE:
return insert_in_edge(p, c, li, lj);
case FACET:
return insert_in_facet(p, c, li);
case CELL:
return insert_in_cell(p, c);
case OUTSIDE_CONVEX_HULL:
return insert_outside_convex_hull(p, c);
case OUTSIDE_AFFINE_HULL:
default:
return insert_outside_affine_hull(p);
}
}
template < class GT, class Tds >
template < class Conflict_tester, class Hidden_points_visitor >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_conflict(const Point & p,
Locate_type lt, Cell_handle c, int li, int /*lj*/,
const Conflict_tester &tester,
Hidden_points_visitor &hider)
{
switch (dimension()) {
case 3:
{
if ((lt == VERTEX) &&
(tester.compare_weight(c->vertex(li)->point(), p)==0) ) {
return c->vertex(li);
}
// If the new point is not in conflict with its cell, it is hidden.
if (!tester.test_initial_cell(c)) {
hider.hide_point(c,p);
return Vertex_handle();
}
// Ok, we really insert the point now.
// First, find the conflict region.
std::vector<Cell_handle> cells;
Facet facet;
cells.reserve(32);
find_conflicts
(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
// Remember the points that are hidden by the conflicting cells,
// as they will be deleted during the insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
// Insertion.
Vertex_handle v = tds()._insert_in_hole(cells.begin(), cells.end(),
facet.first, facet.second);
v->set_point (p);
// Store the hidden points in their new cells.
hider.reinsert_vertices(v);
return v;
}
case 2:
{
// This check is added compared to the 3D case
if (lt == OUTSIDE_AFFINE_HULL)
return insert_outside_affine_hull (p);
if ((lt == VERTEX) &&
(tester.compare_weight(c->vertex(li)->point(), p)==0) ) {
return c->vertex(li);
}
// If the new point is not in conflict with its cell, it is hidden.
if (!tester.test_initial_cell(c)) {
hider.hide_point(c,p);
return Vertex_handle();
}
// Ok, we really insert the point now.
// First, find the conflict region.
std::vector<Cell_handle> cells;
Facet facet;
cells.reserve(32);
find_conflicts
(c, tester, make_triple(Oneset_iterator<Facet>(facet),
std::back_inserter(cells),
Emptyset_iterator()));
// Remember the points that are hidden by the conflicting cells,
// as they will be deleted during the insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
// Insertion.
Vertex_handle v = tds()._insert_in_hole(cells.begin(), cells.end(),
facet.first, facet.second);
v->set_point (p);
// Store the hidden points in their new cells.
hider.reinsert_vertices(v);
return v;
}
default:
{
// dimension() <= 1
if (lt == OUTSIDE_AFFINE_HULL)
return insert_outside_affine_hull (p);
if (lt == VERTEX &&
tester.compare_weight(c->vertex(li)->point(), p) == 0) {
return c->vertex(li);
}
// If the new point is not in conflict with its cell, it is hidden.
if (! tester.test_initial_cell(c)) {
hider.hide_point(c,p);
return Vertex_handle();
}
if (dimension() == 0) {
return hider.replace_vertex(c, li, p);
}
// dimension() == 1;
// Ok, we really insert the point now.
// First, find the conflict region.
std::vector<Cell_handle> cells;
Facet facet;
Cell_handle bound[2];
// corresponding index: bound[j]->neighbor(1-j) is in conflict.
// We get all cells in conflict,
// and remember the 2 external boundaries.
cells.push_back(c);
for (int j = 0; j<2; ++j) {
Cell_handle n = c->neighbor(j);
while ( tester(n) ) {
cells.push_back(n);
n = n->neighbor(j);
}
bound[j] = n;
}
// Insertion.
hider.process_cells_in_conflict(cells.begin(), cells.end());
tds().delete_cells(cells.begin(), cells.end());
// We preserve the order (like the orientation in 2D-3D).
Vertex_handle v = tds().create_vertex();
Cell_handle c0 = tds().create_face(v, bound[0]->vertex(0), Vertex_handle());
Cell_handle c1 = tds().create_face(bound[1]->vertex(1), v, Vertex_handle());
tds().set_adjacency(c0, 1, c1, 0);
tds().set_adjacency(bound[0], 1, c0, 0);
tds().set_adjacency(c1, 1, bound[1], 0);
bound[0]->vertex(0)->set_cell(bound[0]);
bound[1]->vertex(1)->set_cell(bound[1]);
v->set_cell(c0);
v->set_point (p);
hider.reinsert_vertices(v);
return v;
}
}
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_cell(const Point & p, Cell_handle c)
{
CGAL_triangulation_precondition( dimension() == 3 );
CGAL_triangulation_precondition_code
( Locate_type lt;
int i; int j; );
CGAL_triangulation_precondition
( side_of_tetrahedron( p,
c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point(),
lt,i,j ) == ON_BOUNDED_SIDE );
Vertex_handle v = _tds.insert_in_cell(c);
v->set_point(p);
return v;
}
template < class GT, class Tds >
inline
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_facet(const Point & p, Cell_handle c, int i)
{
CGAL_triangulation_precondition( dimension() == 2 || dimension() == 3);
CGAL_triangulation_precondition( (dimension() == 2 && i == 3)
|| (dimension() == 3 && i >= 0 && i <= 3) );
CGAL_triangulation_exactness_precondition_code
( Locate_type lt;
int li; int lj; );
CGAL_triangulation_exactness_precondition
( coplanar( p, c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point() )
&&
side_of_triangle( p,
c->vertex((i+1)&3)->point(),
c->vertex((i+2)&3)->point(),
c->vertex((i+3)&3)->point(),
lt, li, lj) == ON_BOUNDED_SIDE );
Vertex_handle v = _tds.insert_in_facet(c, i);
v->set_point(p);
return v;
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_in_edge(const Point & p, Cell_handle c, int i, int j)
{
CGAL_triangulation_precondition( i != j );
CGAL_triangulation_precondition( dimension() >= 1 && dimension() <= 3 );
CGAL_triangulation_precondition( i >= 0 && i <= dimension()
&& j >= 0 && j <= dimension() );
CGAL_triangulation_exactness_precondition_code( Locate_type lt; int li; );
switch ( dimension() ) {
case 3:
case 2:
{
CGAL_triangulation_precondition( ! is_infinite(c, i, j) );
CGAL_triangulation_exactness_precondition(
collinear( c->vertex(i)->point(),
p,
c->vertex(j)->point() )
&& side_of_segment( p,
c->vertex(i)->point(),
c->vertex(j)->point(),
lt, li ) == ON_BOUNDED_SIDE );
break;
}
case 1:
{
CGAL_triangulation_exactness_precondition( side_of_edge(p, c, lt, li)
== ON_BOUNDED_SIDE );
break;
}
}
Vertex_handle v = _tds.insert_in_edge(c, i, j);
v->set_point(p);
return v;
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_outside_convex_hull(const Point & p, Cell_handle c)
// c is an infinite cell containing p
// p is strictly outside the convex hull
// dimension 0 not allowed, use outside-affine-hull
{
CGAL_triangulation_precondition( dimension() > 0 );
CGAL_triangulation_precondition( c->has_vertex(infinite) );
// the precondition that p is in c is tested in each of the
// insertion methods called from this method
switch ( dimension() ) {
case 1:
{
// // p lies in the infinite edge neighboring c
// // on the other side of li
// return insert_in_edge(p,c->neighbor(1-li),0,1);
return insert_in_edge(p,c,0,1);
}
case 2:
{
Conflict_tester_outside_convex_hull_2 tester(p, this);
Vertex_handle v = insert_conflict(c, tester);
v->set_point(p);
return v;
}
default: // case 3:
{
Conflict_tester_outside_convex_hull_3 tester(p, this);
Vertex_handle v = insert_conflict(c, tester);
v->set_point(p);
return v;
}
}
}
template < class GT, class Tds >
typename Triangulation_3<GT,Tds>::Vertex_handle
Triangulation_3<GT,Tds>::
insert_outside_affine_hull(const Point & p)
{
CGAL_triangulation_precondition( dimension() < 3 );
bool reorient;
switch ( dimension() ) {
case 1:
{
Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex()));
Orientation o = coplanar_orientation(n->vertex(0)->point(),
n->vertex(1)->point(), p);
CGAL_triangulation_precondition ( o != COLLINEAR );
reorient = o == NEGATIVE;
break;
}
case 2:
{
Cell_handle c = infinite_cell();
Cell_handle n = c->neighbor(c->index(infinite_vertex()));
Orientation o = orientation( n->vertex(0)->point(),
n->vertex(1)->point(),
n->vertex(2)->point(), p );
CGAL_triangulation_precondition ( o != COPLANAR );
reorient = o == NEGATIVE;
break;
}
default:
reorient = false;
}
Vertex_handle v = _tds.insert_increase_dimension(infinite_vertex());
v->set_point(p);
if (reorient)
_tds.reorient();
return v;
}
template < class Gt, class Tds >
typename Triangulation_3<Gt,Tds>::Vertex_triple
Triangulation_3<Gt,Tds>::
make_vertex_triple(const Facet& f) const
{
Cell_handle ch = f.first;
int i = f.second;
return Vertex_triple(ch->vertex(vertex_triple_index(i,0)),
ch->vertex(vertex_triple_index(i,1)),
ch->vertex(vertex_triple_index(i,2)));
}
template < class Gt, class Tds >
void
Triangulation_3<Gt,Tds>::
make_canonical(Vertex_triple& t) const
{
int i = (&*(t.first) < &*(t.second))? 0 : 1;
if(i==0) {
i = (&*(t.first) < &*(t.third))? 0 : 2;
} else {
i = (&*(t.second) < &*(t.third))? 1 : 2;
}
Vertex_handle tmp;
switch(i){
case 0: return;
case 1:
tmp = t.first;
t.first = t.second;
t.second = t.third;
t.third = tmp;
return;
default:
tmp = t.first;
t.first = t.third;
t.third = t.second;
t.second = tmp;
}
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
test_dim_down(Vertex_handle v) const
// tests whether removing v decreases the dimension of the triangulation
// true iff
// v is incident to all finite cells/facets
// and all the other vertices are coplanar/collinear in dim3/2.
{
CGAL_triangulation_precondition(dimension() >= 0);
CGAL_triangulation_precondition(! is_infinite(v) );
if (dimension() == 3) {
Finite_cells_iterator cit = finite_cells_begin();
int iv;
if ( ! cit->has_vertex(v,iv) )
return false;
const Point &p1=cit->vertex((iv+1)&3)->point();
const Point &p2=cit->vertex((iv+2)&3)->point();
const Point &p3=cit->vertex((iv+3)&3)->point();
++cit;
for (; cit != finite_cells_end(); ++cit ) {
if ( ! cit->has_vertex(v,iv) )
return false;
for (int i=1; i<4; i++ )
if ( !coplanar(p1,p2,p3,cit->vertex((iv+i)&3)->point()) )
return false;
}
}
else if (dimension() == 2)
{
Finite_facets_iterator cit = finite_facets_begin();
int iv;
if ( ! cit->first->has_vertex(v,iv) )
return false;
const Point &p1 = cit->first->vertex(cw(iv))->point();
const Point &p2 = cit->first->vertex(ccw(iv))->point();
++cit;
for (; cit != finite_facets_end(); ++cit ) {
if ( ! cit->first->has_vertex(v,iv) )
return false;
if ( !collinear(p1, p2, cit->first->vertex(cw(iv))->point()) ||
!collinear(p1, p2, cit->first->vertex(ccw(iv))->point()) )
return false;
}
}
else // dimension() == 1 or 0
return number_of_vertices() == (size_type) dimension() + 1;
return true;
}
template <class Gt, class Tds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt, Tds>::
make_hole_2D(Vertex_handle v, std::list<Edge_2D> &hole, VertexRemover &remover)
{
std::vector<Cell_handle> to_delete;
typename Tds::Face_circulator fc = tds().incident_faces(v);
typename Tds::Face_circulator done(fc);
// We prepare for deleting all interior cells.
// We ->set_cell() pointers to cells outside the hole.
// We push the Edges_2D of the boundary (seen from outside) in "hole".
do {
Cell_handle f = fc;
int i = f->index(v);
Cell_handle fn = f->neighbor(i);
int in = fn->index(f);
f->vertex(cw(i))->set_cell(fn);
fn->set_neighbor(in, Cell_handle());
hole.push_back(Edge_2D(fn, in));
remover.add_hidden_points(f);
to_delete.push_back(f);
++fc;
} while (fc != done);
tds().delete_cells(to_delete.begin(), to_delete.end());
return remover;
}
template <class Gt, class Tds >
template < class VertexRemover >
void
Triangulation_3<Gt, Tds>::
fill_hole_2D(std::list<Edge_2D> & first_hole, VertexRemover &remover)
{
typedef std::list<Edge_2D> Hole;
std::vector<Hole> hole_list;
Cell_handle f, ff, fn;
int i, ii, in;
hole_list.push_back(first_hole);
while( ! hole_list.empty())
{
Hole hole = hole_list.back();
hole_list.pop_back();
// if the hole has only three edges, create the triangle
if (hole.size() == 3) {
typename Hole::iterator hit = hole.begin();
f = (*hit).first; i = (*hit).second;
ff = (* ++hit).first; ii = (*hit).second;
fn = (* ++hit).first; in = (*hit).second;
tds().create_face(f, i, ff, ii, fn, in);
continue;
}
// else find an edge with two finite vertices
// on the hole boundary
// and the new triangle adjacent to that edge
// cut the hole and push it back
// first, ensure that a neighboring face
// whose vertices on the hole boundary are finite
// is the first of the hole
while (1) {
ff = (hole.front()).first;
ii = (hole.front()).second;
if ( is_infinite(ff->vertex(cw(ii))) ||
is_infinite(ff->vertex(ccw(ii)))) {
hole.push_back(hole.front());
hole.pop_front();
}
else
break;
}
// take the first neighboring face and pop it;
ff = (hole.front()).first;
ii = (hole.front()).second;
hole.pop_front();
Vertex_handle v0 = ff->vertex(cw(ii));
Vertex_handle v1 = ff->vertex(ccw(ii));
Vertex_handle v2 = infinite_vertex();
const Point &p0 = v0->point();
const Point &p1 = v1->point();
const Point *p2 = NULL; // Initialize to NULL to avoid warning.
typename Hole::iterator hdone = hole.end();
typename Hole::iterator hit = hole.begin();
typename Hole::iterator cut_after(hit);
// if tested vertex is c with respect to the vertex opposite
// to NULL neighbor,
// stop at the before last face;
hdone--;
for (; hit != hdone; ++hit) {
fn = hit->first;
in = hit->second;
Vertex_handle vv = fn->vertex(ccw(in));
if (is_infinite(vv)) {
if (is_infinite(v2))
cut_after = hit;
}
else { // vv is a finite vertex
const Point &p = vv->point();
if (coplanar_orientation(p0, p1, p) == COUNTERCLOCKWISE) {
if (is_infinite(v2) ||
remover.side_of_bounded_circle(p0, p1, *p2, p, true)
== ON_BOUNDED_SIDE) {
v2 = vv;
p2 = &p;
cut_after = hit;
}
}
}
}
// create new triangle and update adjacency relations
Cell_handle newf;
//update the hole and push back in the Hole_List stack
// if v2 belongs to the neighbor following or preceding *f
// the hole remain a single hole
// otherwise it is split in two holes
fn = (hole.front()).first;
in = (hole.front()).second;
if (fn->has_vertex(v2, i) && i == ccw(in)) {
newf = tds().create_face(ff, ii, fn, in);
hole.pop_front();
hole.push_front(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
fn = (hole.back()).first;
in = (hole.back()).second;
if (fn->has_vertex(v2, i) && i == cw(in)) {
newf = tds().create_face(fn, in, ff, ii);
hole.pop_back();
hole.push_back(Edge_2D(newf, 1));
hole_list.push_back(hole);
}
else{
// split the hole in two holes
newf = tds().create_face(ff, ii, v2);
Hole new_hole;
++cut_after;
while( hole.begin() != cut_after )
{
new_hole.push_back(hole.front());
hole.pop_front();
}
hole.push_front(Edge_2D(newf, 1));
new_hole.push_front(Edge_2D(newf, 0));
hole_list.push_back(hole);
hole_list.push_back(new_hole);
}
}
}
}
template < class Gt, class Tds >
void
Triangulation_3<Gt,Tds>::
make_hole_3D( Vertex_handle v,
std::map<Vertex_triple,Facet>& outer_map,
std::vector<Cell_handle> & hole)
{
CGAL_triangulation_expensive_precondition( ! test_dim_down(v) );
incident_cells(v, std::back_inserter(hole));
for (typename std::vector<Cell_handle>::iterator cit = hole.begin();
cit != hole.end(); ++cit) {
int indv = (*cit)->index(v);
Cell_handle opp_cit = (*cit)->neighbor( indv );
Facet f(opp_cit, opp_cit->index(*cit));
Vertex_triple vt = make_vertex_triple(f);
make_canonical(vt);
outer_map[vt] = f;
for (int i=0; i<4; i++)
if ( i != indv )
(*cit)->vertex(i)->set_cell(opp_cit);
}
}
template < class Gt, class Tds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds>::
remove_dim_down(Vertex_handle v, VertexRemover &remover)
{
CGAL_triangulation_precondition (dimension() >= 0);
// Collect all the hidden points.
for (All_cells_iterator ci = tds().raw_cells_begin();
ci != tds().raw_cells_end(); ++ci)
remover.add_hidden_points(ci);
tds().remove_decrease_dimension(v, infinite_vertex());
// Now try to see if we need to re-orient.
if (dimension() == 2) {
Facet f = *finite_facets_begin();
if (coplanar_orientation(f.first->vertex(0)->point(),
f.first->vertex(1)->point(),
f.first->vertex(2)->point()) == NEGATIVE)
tds().reorient();
}
return remover;
}
template < class Gt, class Tds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds>::
remove_1D(Vertex_handle v, VertexRemover &remover)
{
CGAL_triangulation_precondition (dimension() == 1);
Cell_handle c1 = v->cell();
Cell_handle c2 = c1->neighbor(c1->index(v) == 0 ? 1 : 0);
remover.add_hidden_points(c1);
remover.add_hidden_points(c2);
tds().remove_from_maximal_dimension_simplex (v);
return remover;
}
template < class Gt, class Tds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds>::
remove_2D(Vertex_handle v, VertexRemover &remover)
{
CGAL_triangulation_precondition(dimension() == 2);
std::list<Edge_2D> hole;
make_hole_2D(v, hole, remover);
fill_hole_2D(hole, remover);
tds().delete_vertex(v);
return remover;
}
template < class Gt, class Tds >
template < class VertexRemover >
VertexRemover&
Triangulation_3<Gt,Tds>::
remove_3D(Vertex_handle v, VertexRemover &remover)
{
std::vector<Cell_handle> hole;
hole.reserve(64);
// Construct the set of vertex triples on the boundary
// with the facet just behind
typedef std::map<Vertex_triple,Facet> Vertex_triple_Facet_map;
Vertex_triple_Facet_map outer_map;
Vertex_triple_Facet_map inner_map;
make_hole_3D(v, outer_map, hole);
CGAL_assertion(remover.hidden_points_begin() ==
remover.hidden_points_end() );
// Output the hidden points.
for (typename std::vector<Cell_handle>::iterator
hi = hole.begin(), hend = hole.end(); hi != hend; ++hi)
remover.add_hidden_points(*hi);
bool inf = false;
unsigned int i;
// collect all vertices on the boundary
std::vector<Vertex_handle> vertices;
vertices.reserve(64);
adjacent_vertices(v, std::back_inserter(vertices));
// create a Delaunay triangulation of the points on the boundary
// and make a map from the vertices in remover.tmp towards the vertices
// in *this
Unique_hash_map<Vertex_handle,Vertex_handle> vmap;
Cell_handle ch = Cell_handle();
for(i=0; i < vertices.size(); i++){
if(! is_infinite(vertices[i])){
Vertex_handle vh = remover.tmp.insert(vertices[i]->point(), ch);
ch = vh->cell();
vmap[vh] = vertices[i];
}else {
inf = true;
}
}
if(remover.tmp.dimension()==2){
Vertex_handle fake_inf = remover.tmp.insert(v->point());
vmap[fake_inf] = infinite_vertex();
} else {
vmap[remover.tmp.infinite_vertex()] = infinite_vertex();
}
CGAL_triangulation_assertion(remover.tmp.dimension() == 3);
// Construct the set of vertex triples of remover.tmp
// We reorient the vertex triple so that it matches those from outer_map
// Also note that we use the vertices of *this, not of remover.tmp
if(inf){
for(All_cells_iterator it = remover.tmp.all_cells_begin();
it != remover.tmp.all_cells_end();
++it){
for(i=0; i < 4; i++){
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical(vt);
inner_map[vt]= f;
}
}
} else {
for(Finite_cells_iterator it = remover.tmp.finite_cells_begin();
it != remover.tmp.finite_cells_end();
++it){
for(i=0; i < 4; i++){
Facet f = std::pair<Cell_handle,int>(it,i);
Vertex_triple vt_aux = make_vertex_triple(f);
Vertex_triple vt(vmap[vt_aux.first],vmap[vt_aux.third],vmap[vt_aux.second]);
make_canonical(vt);
inner_map[vt]= f;
}
}
}
// Grow inside the hole, by extending the surface
while(! outer_map.empty()){
typename Vertex_triple_Facet_map::iterator oit = outer_map.begin();
while(is_infinite(oit->first.first) ||
is_infinite(oit->first.second) ||
is_infinite(oit->first.third)){
++oit;
// otherwise the lookup in the inner_map fails
// because the infinite vertices are different
}
typename Vertex_triple_Facet_map::value_type o_vt_f_pair = *oit;
Cell_handle o_ch = o_vt_f_pair.second.first;
unsigned int o_i = o_vt_f_pair.second.second;
typename Vertex_triple_Facet_map::iterator iit =
inner_map.find(o_vt_f_pair.first);
CGAL_triangulation_assertion(iit != inner_map.end());
typename Vertex_triple_Facet_map::value_type i_vt_f_pair = *iit;
Cell_handle i_ch = i_vt_f_pair.second.first;
unsigned int i_i = i_vt_f_pair.second.second;
// create a new cell and glue it to the outer surface
Cell_handle new_ch = tds().create_cell();
new_ch->set_vertices(vmap[i_ch->vertex(0)], vmap[i_ch->vertex(1)],
vmap[i_ch->vertex(2)], vmap[i_ch->vertex(3)]);
o_ch->set_neighbor(o_i,new_ch);
new_ch->set_neighbor(i_i, o_ch);
// for the other faces check, if they can also be glued
for(i = 0; i < 4; i++){
if(i != i_i){
Facet f = std::pair<Cell_handle,int>(new_ch,i);
Vertex_triple vt = make_vertex_triple(f);
make_canonical(vt);
std::swap(vt.second,vt.third);
typename Vertex_triple_Facet_map::iterator oit2 = outer_map.find(vt);
if(oit2 == outer_map.end()){
std::swap(vt.second,vt.third);
outer_map[vt]= f;
} else {
// glue the faces
typename Vertex_triple_Facet_map::value_type o_vt_f_pair2 = *oit2;
Cell_handle o_ch2 = o_vt_f_pair2.second.first;
int o_i2 = o_vt_f_pair2.second.second;
o_ch2->set_neighbor(o_i2,new_ch);
new_ch->set_neighbor(i, o_ch2);
outer_map.erase(oit2);
}
}
}
outer_map.erase(oit);
}
tds().delete_vertex(v);
tds().delete_cells(hole.begin(), hole.end());
return remover;
}
template < class Gt, class Tds >
template < class VertexRemover >
void
Triangulation_3<Gt, Tds>::
remove(Vertex_handle v, VertexRemover &remover) {
CGAL_triangulation_precondition( v != Vertex_handle());
CGAL_triangulation_precondition( !is_infinite(v));
CGAL_triangulation_expensive_precondition( tds().is_vertex(v) );
if (test_dim_down (v)) {
remove_dim_down (v, remover);
}
else {
switch (dimension()) {
case 1: remove_1D (v, remover); break;
case 2: remove_2D (v, remover); break;
case 3: remove_3D (v, remover); break;
default:
CGAL_triangulation_assertion (false);
}
}
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_valid(bool verbose, int level) const
{
if ( ! _tds.is_valid(verbose,level) ) {
if (verbose)
std::cerr << "invalid data structure" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
if ( infinite_vertex() == Vertex_handle() ) {
if (verbose)
std::cerr << "no infinite vertex" << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
switch ( dimension() ) {
case 3:
{
Finite_cells_iterator it;
for ( it = finite_cells_begin(); it != finite_cells_end(); ++it )
is_valid_finite(it, verbose, level);
break;
}
case 2:
{
Finite_facets_iterator it;
for ( it = finite_facets_begin(); it != finite_facets_end(); ++it )
is_valid_finite(it->first,verbose,level);
break;
}
case 1:
{
Finite_edges_iterator it;
for ( it = finite_edges_begin(); it != finite_edges_end(); ++it )
is_valid_finite(it->first,verbose,level);
break;
}
}
if (verbose)
std::cerr << "valid triangulation" << std::endl;
return true;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_valid(Cell_handle c, bool verbose, int level) const
{
if ( ! _tds.is_valid(c,verbose,level) ) {
if (verbose) {
std::cerr << "combinatorially invalid cell";
for (int i=0; i <= dimension(); i++ )
std::cerr << c->vertex(i)->point() << ", ";
std::cerr << std::endl;
}
CGAL_triangulation_assertion(false);
return false;
}
if ( ! is_infinite(c) )
is_valid_finite(c, verbose, level);
if (verbose)
std::cerr << "geometrically valid cell" << std::endl;
return true;
}
template < class GT, class Tds >
bool
Triangulation_3<GT,Tds>::
is_valid_finite(Cell_handle c, bool verbose, int) const
{
switch ( dimension() ) {
case 3:
{
if ( orientation(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point(),
c->vertex(3)->point()) != POSITIVE ) {
if (verbose)
std::cerr << "badly oriented cell "
<< c->vertex(0)->point() << ", "
<< c->vertex(1)->point() << ", "
<< c->vertex(2)->point() << ", "
<< c->vertex(3)->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 2:
{
if (coplanar_orientation(c->vertex(0)->point(),
c->vertex(1)->point(),
c->vertex(2)->point()) != POSITIVE) {
if (verbose)
std::cerr << "badly oriented face "
<< c->vertex(0)->point() << ", "
<< c->vertex(1)->point() << ", "
<< c->vertex(2)->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
break;
}
case 1:
{
const Point & p0 = c->vertex(0)->point();
const Point & p1 = c->vertex(1)->point();
Vertex_handle v = c->neighbor(0)->vertex(c->neighbor(0)->index(c));
if ( ! is_infinite(v) )
{
if ( collinear_position(p0, p1, v->point()) != MIDDLE ) {
if (verbose)
std::cerr << "badly oriented edge "
<< p0 << ", " << p1 << std::endl
<< "with neighbor 0"
<< c->neighbor(0)->vertex(1-c->neighbor(0)->index(c))
->point()
<< ", " << v->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
v = c->neighbor(1)->vertex(c->neighbor(1)->index(c));
if ( ! is_infinite(v) )
{
if ( collinear_position(p1, p0, v->point()) != MIDDLE ) {
if (verbose)
std::cerr << "badly oriented edge "
<< p0 << ", " << p1 << std::endl
<< "with neighbor 1"
<< c->neighbor(1)->vertex(1-c->neighbor(1)->index(c))
->point()
<< ", " << v->point() << std::endl;
CGAL_triangulation_assertion(false);
return false;
}
}
break;
}
}
return true;
}
namespace CGALi {
// Internal function used by operator==.
template < class GT, class Tds1, class Tds2 >
bool
test_next(const Triangulation_3<GT, Tds1> &t1,
const Triangulation_3<GT, Tds2> &t2,
typename Triangulation_3<GT, Tds1>::Cell_handle c1,
typename Triangulation_3<GT, Tds2>::Cell_handle c2,
std::map<typename Triangulation_3<GT, Tds1>::Cell_handle,
typename Triangulation_3<GT, Tds2>::Cell_handle> &Cmap,
std::map<typename Triangulation_3<GT, Tds1>::Vertex_handle,
typename Triangulation_3<GT, Tds2>::Vertex_handle> &Vmap)
{
// This function tests and registers the 4 neighbors of c1/c2,
// and recursively calls itself over them.
// Returns false if an inequality has been found.
// Precondition: c1, c2 have been registered as well as their 4 vertices.
CGAL_triangulation_precondition(t1.dimension() >= 2);
CGAL_triangulation_precondition(Cmap[c1] == c2);
CGAL_triangulation_precondition(Vmap.find(c1->vertex(0)) != Vmap.end());
CGAL_triangulation_precondition(Vmap.find(c1->vertex(1)) != Vmap.end());
CGAL_triangulation_precondition(Vmap.find(c1->vertex(2)) != Vmap.end());
CGAL_triangulation_precondition(t1.dimension() == 2 ||
Vmap.find(c1->vertex(3)) != Vmap.end());
typedef Triangulation_3<GT, Tds1> Tr1;
typedef Triangulation_3<GT, Tds2> Tr2;
typedef typename Tr1::Vertex_handle Vertex_handle1;
typedef typename Tr1::Cell_handle Cell_handle1;
typedef typename Tr2::Vertex_handle Vertex_handle2;
typedef typename Tr2::Cell_handle Cell_handle2;
typedef typename std::map<Cell_handle1, Cell_handle2>::const_iterator Cit;
typedef typename std::map<Vertex_handle1,
Vertex_handle2>::const_iterator Vit;
for (int i=0; i <= t1.dimension(); ++i) {
Cell_handle1 n1 = c1->neighbor(i);
Cit cit = Cmap.find(n1);
Vertex_handle1 v1 = c1->vertex(i);
Vertex_handle2 v2 = Vmap[v1];
Cell_handle2 n2 = c2->neighbor(c2->index(v2));
if (cit != Cmap.end()) {
// n1 was already registered.
if (cit->second != n2)
return false;
continue;
}
// n1 has not yet been registered.
// We check that the new vertices match geometrically.
// And we register them.
Vertex_handle1 vn1 = n1->vertex(n1->index(c1));
Vertex_handle2 vn2 = n2->vertex(n2->index(c2));
Vit vit = Vmap.find(vn1);
if (vit != Vmap.end()) {
// vn1 already registered
if (vit->second != vn2)
return false;
}
else {
if (t2.is_infinite(vn2))
return false; // vn1 can't be infinite,
// since it would have been registered.
if (t1.geom_traits().compare_xyz_3_object()(vn1->point(),
vn2->point()) != 0)
return false;
// We register vn1/vn2.
Vmap.insert(std::make_pair(vn1, vn2));
}
// We register n1/n2.
Cmap.insert(std::make_pair(n1, n2));
// We recurse on n1/n2.
if (!test_next(t1, t2, n1, n2, Cmap, Vmap))
return false;
}
return true;
}
} // namespace CGALi
template < class GT, class Tds1, class Tds2 >
bool
operator==(const Triangulation_3<GT, Tds1> &t1,
const Triangulation_3<GT, Tds2> &t2)
{
typedef typename Triangulation_3<GT, Tds1>::Vertex_handle Vertex_handle1;
typedef typename Triangulation_3<GT, Tds1>::Cell_handle Cell_handle1;
typedef typename Triangulation_3<GT, Tds2>::Vertex_handle Vertex_handle2;
typedef typename Triangulation_3<GT, Tds2>::Cell_handle Cell_handle2;
typedef typename Triangulation_3<GT, Tds1>::Point Point;
typedef typename Triangulation_3<GT, Tds1>::Geom_traits::Equal_3 Equal_3;
typedef typename Triangulation_3<GT, Tds1>::Geom_traits::Compare_xyz_3 Compare_xyz_3;
Equal_3 equal = t1.geom_traits().equal_3_object();
Compare_xyz_3 cmp1 = t1.geom_traits().compare_xyz_3_object();
Compare_xyz_3 cmp2 = t2.geom_traits().compare_xyz_3_object();
// Some quick checks.
if (t1.dimension() != t2.dimension()
|| t1.number_of_vertices() != t2.number_of_vertices()
|| t1.number_of_cells() != t2.number_of_cells())
return false;
int dim = t1.dimension();
// Special case for dimension < 1.
// The triangulation is uniquely defined in these cases.
if (dim < 1)
return true;
// Special case for dimension == 1.
if (dim == 1) {
// It's enough to test that the points are the same,
// since the triangulation is uniquely defined in this case.
using namespace boost;
std::vector<Point> V1 (t1.points_begin(), t1.points_end());
std::vector<Point> V2 (t2.points_begin(), t2.points_end());
std::sort(V1.begin(), V1.end(), bind(cmp1, _1, _2) == NEGATIVE);
std::sort(V2.begin(), V2.end(), bind(cmp2, _1, _2) == NEGATIVE);
return V1 == V2;
}
// We will store the mapping between the 2 triangulations vertices and
// cells in 2 maps.
std::map<Vertex_handle1, Vertex_handle2> Vmap;
std::map<Cell_handle1, Cell_handle2> Cmap;
// Handle the infinite vertex.
Vertex_handle1 v1 = t1.infinite_vertex();
Vertex_handle2 iv2 = t2.infinite_vertex();
Vmap.insert(std::make_pair(v1, iv2));
// We pick one infinite cell of t1, and try to match it against the
// infinite cells of t2.
Cell_handle1 c = v1->cell();
Vertex_handle1 v2 = c->vertex((c->index(v1)+1)%(dim+1));
Vertex_handle1 v3 = c->vertex((c->index(v1)+2)%(dim+1));
Vertex_handle1 v4 = c->vertex((c->index(v1)+3)%(dim+1));
const Point &p2 = v2->point();
const Point &p3 = v3->point();
const Point &p4 = v4->point();
std::vector<Cell_handle2> ics;
t2.incident_cells(iv2, std::back_inserter(ics));
for (typename std::vector<Cell_handle2>::const_iterator cit = ics.begin();
cit != ics.end(); ++cit) {
int inf = (*cit)->index(iv2);
if (equal(p2, (*cit)->vertex((inf+1)%(dim+1))->point()))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+1)%(dim+1))));
else if (equal(p2, (*cit)->vertex((inf+2)%(dim+1))->point()))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+2)%(dim+1))));
else if (dim == 3 &&
equal(p2, (*cit)->vertex((inf+3)%(dim+1))->point()))
Vmap.insert(std::make_pair(v2, (*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v2.
if (equal(p3, (*cit)->vertex((inf+1)%(dim+1))->point()))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+1)%(dim+1))));
else if (equal(p3, (*cit)->vertex((inf+2)%(dim+1))->point()))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+2)%(dim+1))));
else if (dim == 3 &&
equal(p3, (*cit)->vertex((inf+3)%(dim+1))->point()))
Vmap.insert(std::make_pair(v3, (*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v3.
if (dim == 3) {
if (equal(p4, (*cit)->vertex((inf+1)%(dim+1))->point()))
Vmap.insert(std::make_pair(v4,
(*cit)->vertex((inf+1)%(dim+1))));
else if (equal(p4, (*cit)->vertex((inf+2)%(dim+1))->point()))
Vmap.insert(std::make_pair(v4,
(*cit)->vertex((inf+2)%(dim+1))));
else if (equal(p4, (*cit)->vertex((inf+3)%(dim+1))->point()))
Vmap.insert(std::make_pair(v4,
(*cit)->vertex((inf+3)%(dim+1))));
else
continue; // None matched v4.
}
// Found it !
Cmap.insert(std::make_pair(c, *cit));
break;
}
if (Cmap.size() == 0)
return false;
// We now have one cell, we need to propagate recursively.
return CGALi::test_next(t1, t2,
Cmap.begin()->first, Cmap.begin()->second, Cmap, Vmap);
}
template < class GT, class Tds1, class Tds2 >
inline
bool
operator!=(const Triangulation_3<GT, Tds1> &t1,
const Triangulation_3<GT, Tds2> &t2)
{
return ! (t1 == t2);
}
CGAL_END_NAMESPACE
#endif // CGAL_TRIANGULATION_3_H
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